Group Theory and the Megaminx
DOI:
https://doi.org/10.61173/j9jt7y19Keywords:
Group TheoryAbstract
The Rubik’s cube is famous for its complexity, and its applications with the group theory also amaze mathematicians. Based on the Rubik’s cube, megaminx is created. Similarly, it can be applied with group theory. This work aims to define the structure of megaminx in terms of the Group Theory and deduce the full conditions for megaminx to stay in a valid configuration of it.
References
[1] . Lindsey Daniels. Group theory and the rubik’s cube. 1. If (σ, τ, x, y ) is a configuration of megaminx such that Lakehead Universityc, 2014. σ sgnτ, ∑ xi ≡ 0 ( mod 3) and sgn= ∑y i ≡ 0 ( mod 2 ) , then [2]. David Steven Dummit and Richard M Foote. Abstract t h e r e m u s t b e a m o v e m e n t P ∈G s o t h a t algebra, volume 3. Wiley Hoboken, 2004.
[3] . David Joyner. Adventures in group theory: Rubik’s Cube, (σ, τ, x, y ) ⋅ P= (1, τ ', x ', y ') w i t h Merlin’s machine, and other mathematical toys. JHU Press, = sgnτ ' 1, ∑ xi ' ≡ 0 ( mod 3) and ∑y '≡0 i (mod2), which 2008. means that the locations of the corner cubies are right. [4]. JJ Chen. Group theory and the rubik’s cube, 2004.
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